**Date & Time:** Wednesday, July 1, 2015, 16:00-17:00.

**Venue:** Ramanujan Hall

**Speaker:** M. Ram Murty, Queens University

**Title:** Consecutive squarefull numbers

**Abstract:** A natural number is called squarefull if whenever a prime p
divides it, so does p^2. Erdos conjectured that the number of squarefull
numbers less than x is bounded by (log x)^A for some A positive. We will
prove this conjecture assuming the ABC conjecture and also obtain some
unconditional results. We also relate this problem to the study of
fundamental units in real quadratic fields. This is joint work with Kevser
Aktas.